The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential in-equality techniques, some su...The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential in-equality techniques, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of the system are obtained. The criteria do not require the activation functions to be differentiable or monotone nondecreasing. Some stability results from previous works are extended and improved. Comparisons are made to demonstrate the advantage of our results.展开更多
This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model ar...This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.展开更多
The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability o...The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability of equilibria and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation due to the two-parameter geometric criteria developed by Ma, Feng and Lu [Discrete Contin. Dyn. Syst. Set B 9 （2008） 397-413]. The global stability of the positive equilibrium is inves- tigated by the comparison theorem. Furthermore, local stability of steady states and the existence of Hopf bifurcation for prey harvesting are also considered. Numerical simulations are given to illustrate our theoretical findings.展开更多
In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with di...In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with different edges on transmission rate as epidemics prevail. Furthermore, by constructing Lyapunov function, we prove that the disease-free equilibrium E^0 is globally asymptotically stable as the epidemic threshold R^＊〈 1. When R^＊ 〉 1, we obtain the permanence of epidemic and the local stability of endemic equilibrium E＊. Finally, one can find a good agreement between numerical simulations and our analytical results.展开更多
In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease^free equilibrium and the endemic equilibrium....In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease^free equilibrium and the endemic equilibrium. Furthermore, by using comparison method, we obtain the global stability of these equilibrium points under certain parametric con- ditions. Some illustrative examples are provided to support our theoretical discussion.展开更多
基金National Natural Science Foundation of China (No70471049)
文摘The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential in-equality techniques, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of the system are obtained. The criteria do not require the activation functions to be differentiable or monotone nondecreasing. Some stability results from previous works are extended and improved. Comparisons are made to demonstrate the advantage of our results.
文摘This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.
文摘The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability of equilibria and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation due to the two-parameter geometric criteria developed by Ma, Feng and Lu [Discrete Contin. Dyn. Syst. Set B 9 （2008） 397-413]. The global stability of the positive equilibrium is inves- tigated by the comparison theorem. Furthermore, local stability of steady states and the existence of Hopf bifurcation for prey harvesting are also considered. Numerical simulations are given to illustrate our theoretical findings.
基金This work is supported by the National Natural Science Foundation of China under Grant 61174039. The authors would like to thank the editor and the reviewers for their constructive comments and suggestions to improve the quality of this paper.
文摘In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with different edges on transmission rate as epidemics prevail. Furthermore, by constructing Lyapunov function, we prove that the disease-free equilibrium E^0 is globally asymptotically stable as the epidemic threshold R^＊〈 1. When R^＊ 〉 1, we obtain the permanence of epidemic and the local stability of endemic equilibrium E＊. Finally, one can find a good agreement between numerical simulations and our analytical results.
文摘In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease^free equilibrium and the endemic equilibrium. Furthermore, by using comparison method, we obtain the global stability of these equilibrium points under certain parametric con- ditions. Some illustrative examples are provided to support our theoretical discussion.
